Questions tagged [computational-mathematics]

Question 1

Suppose $C$ is the plane curve cut out by the equation $$ u^2 + \frac{8}{3} uv + v^2 = \frac{5}{3} - u^2 v^2 . $$ Can you provide an explicit change of coordinates that puts this curve in Edwards form,...

Question 2

I've got the following system to solve \begin{align} \begin{bmatrix} A & B \\ B^* & C \end{bmatrix} \begin{bmatrix} u \\ p \end{bmatrix} = \begin{bmatrix} 0 \\ g \end{bmatrix}, \end{align} ...

Question 3

Let $E/\mathbb{Q}$ be an elliptic curve with complex multiplication by $\mathbb{Q}(i)$, e.g. any curve of the form $E:y^2 = x^3 + Ax$ with $A \in \mathbb{Q}^\times$. I would like to compute generators ...

Question 4

I am checking an intersection of two properties: is a square-free Carmichael number, i.e. composite, square-free, and for every prime we have (Korselt). has two distinct representations as a sum of ...

Question 5

Consider the equation: $$ \partial_tu=D\partial_{xx}^2u $$ with reflecting boundary condition at $x=0$ and with $u(x,0)=\delta(x)$ as an initial distribution. First question: How should I understand a ...

Question 6

I'm working with a scriptable 3-D rendering tool that, due to various rounding and binary representation errors in point arithmetic will throw errors at extremely rare but always inopportune times. ...

Question 7

Consider the following Linear Program...$$\text{minimize}_{\vec x}\ \ \ \ x_1 - 2x_2 \\ \ \text{s.t.}\ \ \ \ \ \ 4x_1 + 6x_2 \leq 1 \\ x_2 \leq 7 \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3x_1 - x_2 = -2$$A ...

Question 8

I would like to calculate $$\frac{\partial (\mathbf F^{-1})^T}{\partial \mathbf F}$$ I know that $$\frac{\partial (F^{-1})_{ab}}{\partial F{ij}} = - (F^{-1})_{ai} \,(F^{-1})_{jb}$$ Also, if $[\mathbf ...

Question 9

I have been experimenting with a family of Eratosthenes-like sieves that seem to generate long streaks of primes before producing the first composite. I would like to ask if something like this is ...

Question 10

I strongly suspect this question has a very straightforward answer. Let $M = \mathbb{Q}(\sqrt{a_1},\dots,\sqrt{a_k})$ be a large multiquadratic field. In this setup we assume it is infeasible to ...

Question 11

I want to calculate frame error rate(FER for short) of BCH Code in high precision, the formula is: $$FER = 1 - \sum_{i=0}^t {n \choose i} p^i(1-p)^{n-i}$$ where $n = 2560, t = 41$, $p = 10^{-4}$ to $...

Question 12

=(-2)^0.333 = #NUM! =(-2)^(1/3) = -1.25992 Is this a math thing or a coding thing? Why does expressing the power as a decimal produce an error, whereas as a fraction it finds the value?

Question 13

I am working on some problem on toric arrangements at the crossroad between topology, combinatorics and algebraic geometry. $\textbf{Setting}$ Let $m,n\geq1$ and let \begin{equation*}\mathcal{S}=\left\...

Question 14

I need to calculate the volume (and centroid, but techniques for both seem to be fairly similar) of the intersection between the unit cube defined by $0 \leq x,y,z \leq 1$ and the halfspace defined by ...

Question 15

Problem A trapezoidal prism is "cut" by an infinite plane. The plane passes through the center of the trapezoidal prism, and the normal vector to the plane is known. The prism is isosceles (...

Stack Exchange Network

Questions tagged [computational-mathematics]

Converting an elliptic curve to Edwards form

How to solve the following system of equations without using inverse matrices?

Computing large division fields of elliptic curves with CM

Are there any other square-free Carmichael numbers $\leq10^8$ with two distinct positive two-cube representations besides $1729$?

Diffusion equation after one time-step

How to overcome Cartesian/Polar round trip anomalies in 64-bit IEEE floating-point numbers

Linear Program Duality Confusion

How to compute the derivative of transpose of inverse matrix of non symmetric matrix to matrix

A scalable sieve generating long prime streaks

Algorithm for ideal sum/relative norm in multiquadratic field

How to calculate frame error rate of BCH Code in very high precision?

Why can't MS excel calculate -2^0.333, but it can calculate -2^(1/3)? [closed]

Toric arrangements and system of polynomial equations

Volume/centroid of unit cube cut by plane

Quickly determine (or approximate) surface area of intersection between an infinite plane and a trapezoidal prism

Hot Network Questions